Cold Polar Molecules and their Applications for Quantum Information H.P. Büchler Theoretische Physik III, Universität Stuttgart, Germany
Cold Polar Molecules and their Applications for Quantum
Information
H.P. BüchlerTheoretische Physik III, Universität Stuttgart, Germany
Outline
Introduction to polar molecules
- quantum melting transition betweena crystal of and a superfluid
AMO- solid state interface
- solid state quantum processor- molecular quantum memory
Spin toolbox
- polar molecules with spin- realization of Kitaev model- three-body interactions
Polar molecules
Why hetronuclear polar molecules?
- coupling to optical and microwave fields
- permanent dipole moment
- trapping/cooling- internal states
- strong dipole-dipole interaction
- long-range interaction
dipole moment
- electronic excitations
- vibrational excitations
- rotational excitations(microwave fields)
- electron spin- nuclear spin
Polar moleculesHetronuclear Molecules
dipole moment
rotational and vibrational ground state
vibrational levels
electronic levels
vibrational levels
Polar molecule
Sr2+
O2–
req = 1.919 Ǻd = 8.9 D
X 1Σ+ ... electronic groundstate:S=0 ... closed shell (..9σ2 10σ2 4π4 )
req = 1.919 Ǻ ... equilibrium distanced = 8.900 D ... dipole-moment
ωeq = 19.586 THz ... vibrational const.Beq = 10.145 GHz ... rotational I=0 ... no nuclear momenta for 88SrO, 86SrO
heteronuclear molecule with strong persistentdipole moment in electronic groundstate.
Sr2+O2–... ionic binding
Rydberg-Klein-Rees (RKR)-potentials(R. Skelton et al., 2003)
Polar molecules
dipole moment
Polar molecules in the electronic, vibrational, androtational ground state
- permanent dipole moment:
- polarizable with static electricfield, and microwave fields
- interactions are increased by
compared to magnetic dipole interactions
Strong dipole-dipole interactions tunable with
external fields
Experimental status
- Polar molecules in the rotational and vibrational ground state
- cooling and trapping techniquesbeeing developement:
- hetronuclear molecules, e.g., SrO, RbCs, LiCs, Sr F
Polar molecules
Raman laser /spontaneous emission
rotational and vibrational ground state
- cooling of polar molecules:D. De Mille, YaleJ. Doyle, Harvard G. Rempe, MunichG. Meijer, BerlinJ. Ye, JILA
- photo association(all cold atom labs)
Polar molecule
Low energy description
- rigid rotor in an electric field
- anharmonic spectrum- electric dipole transition
- microwave transition frequencies- no spontaneous emission
Accessible via microwave
dipole moment
rotation of the molecule
: angular momentum
: dipole operator
Static electric field
- internal Hamilton
- finite averaged dipole moment
Polar moleculeDipole matrix elements
- basis states
- dipole operator:
- matrix elements
Clebsch Gordan coefficient
Polar molecule
rigid rotor
spin-rotation hyperfine
Polar molecules with spin CaF
- electronic spin
- nuclear spin
spin along molecular axes
Interaction between polar molecules
Hamiltonian
Without external drive
- van der Waals attraction
kineticenergy
trappingpotential
rigid rotor
electric field
interaction potential
Static electric field
- internal Hamilton
- finite averaged dipole moment
Dipole-dipole interaction
Dipole-dipole interaction
- anisotropic interaction- long-range
repulsionattraction
Weak Dipole-dipole interaction
- short-range interaction: - pseudo-potential- s-wave scattering length
- long range part via dipole-dipole interaction
Dipole-dipole interaction
Dipole-dipole interaction
- anisotropic interaction- long-range
Instability in the many-body system
attraction
- collaps of the system for increasing dipole interaction(Pfau ‘07)
- roton softening- supersolids? (Goral et. al. ‘02, L. Santos et al. ‘03, Shlyapnikov ‘06)
Stability:
- strong interactions
- confining into 2Dby an optical lattice
repulsionattraction
confining potential
oscillator wavefunction
Stability via transverse confiningEffective interaction
- interaction potential with transverse trapping potential
- characteristic length scale
- potential barrier: larger than kinetic energy
Tunneling rate:
- semi-classical rate(instanton techniques)
- Euclidean action of the instanton trajectory
attempt frequency
numericalfactor: bound
states
kineticenergies
Crystalline phase